the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Jan 2025
Effect of interplanetary shock waves on turbulence parameters
Abstract. We have performed an extensive statistical investigation of how interplanetary fast forward shocks affect certain turbulence parameters β namely, the normalised cross-helicity (ππ), residual energy (ππ) and magnetic helicity (ππ). A total of 371 shocks detected by Wind at 1 au and seven shocks by Solar Orbiter below 0.5 au have been analysed. We explore how the aforementioned turbulence parameters and their variations across the shock depend on the shock characteristics, i.e. the gas compression ratio, upstream plasma beta, velocity jump and shock angle. We find that in the shock vicinity, fluctuations tend to show outward imbalance (measured by ππ), dominance of magnetic energy (negative ππ) and zero ππ when averaged over longer periods. The tendency for imbalance and high AlfvΓ©nicity (ππ βΌ 0) increases with increasing shock velocity jump, and decreasing upstream beta and shock angle. Shocks with large velocity jumps and gas compression ratio have considerably more balanced (ππ βΌ 0) and less AlfvΓ©nic fluctuations in their downstream than upstream, presumably resulting both from AlfvΓ©nic fluctuations not passing to the downstream and generation of new compressive fluctuations. We also find that frequency of periods fulfilling the criteria for AlfvΓ©n fluctuations (AF) usually decreases, while those meeting the criteria for small-scale flux ropes (SFR) increases from upstream to downstream. The occurrence of AF-like periods peaks for quasi-parallel shocks with large velocity jump, and small upstream beta values. The occurrence of SFR in turn increases with increasing gas compression ratio and upstream beta. The shocks observed by Solar Orbiter at 0.3 β 0.5 au feature overall similar distributions of turbulence parameters and similar upstream-to-downstream changes as detected at 1 au. These results are relevant for understanding turbulence and charged-particle acceleration at collisionless shocks.
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RC1: 'Comment on egusphere-2024-3564', Anonymous Referee #1, 31 Jan 2025
This paper investigates the relation between upstream and downstream turbulence across interplanetary shocks in the solar wind nearer to the sun ased on solar orbiter observations. There is a wealth of investigations of such a relation substantially farther away from the sun around 1 AU or farther out, while the present paper deals with a region closer to the source region of both interplanetary shocks and also turbulence inside of 0.5 AU a region attributed to a highly dynamic original state of the solar wind though not yet the real source region which is expected to be farther inward inside of the 0.3 AU noch covered by the present observations.
This work in order to inverstigate the relations between intrplanetary travelling shocks and solar wind turbulence ingeneral i.e. its magnetic and non-magnetic components, defines three (normalized) parameters to characterize these relations. These are the ordinary and magnetic cross helicities and residual energy which the authors investigate in the regions upstream and downstream of a large number of observed shocks in order to obtain statistically based general properties of the effect of shocks on turbulence or vice versa turbulence on shocks, but the emphasis is on the former effect assuming that the shocks are violently generated and affect the turbulence wwhile the turbulent effect on the shock properties would be a smaller effect. This may be true even in the regions closer to the sun under investigation as turbulence in the fast streaming solar wind far away from boundaries (assuming the shock front themselves do for the fast stream not represent tangential boundaries which seems to be the case) is of substantially smaller amplitude than the shock pulse in both the fuid and magnetic components.
There is a large amount of standard calculations in determining the above mentioned parameters. Interestng concerning magnetic effects is the distinction between small-scale flux ropes and alfvenic fluctutions, the latter practically transverse magnetic turbulence fluctuations while the former including everything else. Usually flux ropes in space physics are reserved for three-dimensional or localized reconnection events while here the simply account for non-alfvenic magnetic turbulence whether cause in any way by turbulnece which in turbulence may indeed be the case on wide scales related to local reconnection effects in small-scale current sheets which have, in teh turbulence in the magnetosheeth been identified and have also been proposed as the basic dissipation mechanism of plasma turbulence. So those flux ropeds, concernong turbulence could indeed be related to the dissipation range of turbulence which in collisionless plasma is far above the molecular level somewhere around the ion and electron inertial lengths. Large flux ropes would then contribute to dissipation at the ion scale narrow one to the ultimate dissipation at the electron scale. It is not entirely clear whether the present inestigation can indeed resolve that scale. However this is of lesser importance as the interest of the authors is not in those dissipation effect than rather in the relation between turbuence and shocks.
The results of thee investigations are quite complex and given in a lage number of instructive figures underr the prevalent conditions of the used data sets. As expected, around the shock the energy in the turbulent fluctuations is determined by the magnetic fluctuations with the shock front forming a bundary to the turublence. Clearly alfvenic turbulence prpagating parallel/antiparallel to the shock is capable of passing across the shock. It is , however, also cler that an inestigation of this statistical kind does not provide information about the physical mechanisms of turbulence generation inside the shock.
Altogether this paper provides a rather interesting background information for the average properties of the three turbulence parameters defined in the beginning upstream of, downstream, and at a strong shock front travelling in the magnetized solar wind outward from the sun, In the domain investigated it seems that the shocks are strong enough to confine much of the turbulence to downstream. This is known to change farther downstream around and beyond 1 au indicatin that on the way fartherdownstream the turbulence manages to pass across the sshock during and with the flow.
In my opinion there is not much to say neither ttto the method nor to the statistical results which are interesting in themselves. It to some extent round up our icture of turbulence in the solar wind this ttime in presence of sshocks nearer to the sun.
My tendency is to accept the paper almost in its present form for publicationj saving myself from artificially criticizing anything on style or where the presentation could be made clearer. For background papers of this kind βimprovementsβ as someone would call it, make little sense. They serve the community by presenting the required information.
Citation: https://doi.org/10.5194/egusphere-2024-3564-RC1 -
AC1: 'Reply on RC1', Emilia Kilpua, 24 Mar 2025
We thank the reviewer for careful reading of our manuscript and favorable review. We have made some small changes to the paper based on the Reviewer #2 remarks.
Citation: https://doi.org/10.5194/egusphere-2024-3564-AC1
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AC1: 'Reply on RC1', Emilia Kilpua, 24 Mar 2025
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RC2: 'Comment on egusphere-2024-3564', Anonymous Referee #2, 17 Feb 2025
The study analyzes how interplanetary fast-forward shocks influence turbulence parameters using data from Wind (1 AU) and Solar Orbiter (0.3β0.5 AU). It reproduces the previously known features of upstream solar wind turbulence (predominantly outward imbalance, magnetic energy dominance) and investigates the changes in these parameters with respect to shock characteristics such as velocity jump and plasma beta. Furthermore, the authors have found that the occurrence rate of AlfvΓ©nic fluctuations decreases downstream, while the occurrence rate of small-scale flux ropes increases. The results are consistent across distances and contribute to understanding turbulence and particle acceleration in collisionless shocks, as well as theories of fluctuation transmission across a shock front.
The paper reads very well and contains only a small number of inaccuracies/typos, given its length and the number of figures. Below, I list a few minor comments that should enhance the overall high quality of the manuscript.
Minor Comments
Lines 61-64:
I believe this sentence should be phrased more clearly. While the residual energy increases with heliocentric distance, the imbalance of the inertial range cross-helicity decreasesβi.e., it approaches zero with increasing heliocentric distance. See, for example, Figure 63 in Bruno and Carbone (2013).
Line 236:
Upon closer inspection of Figure 4, it appears that the running median differs for r_g, beta_u, etc. For example, for r_g, the black and grey curves should end between the 20th and 21st data points. However, there are only four points to the right of the curveβs endings, which suggests that the running median is calculated over eight points. For beta_u, there appear to be approximately 16 points, suggesting that the median is calculated over ~32 points. Could the authors comment on this or improve the figures?
If a mean is calculated over the x-values while the median is applied to the y-values, I suggest changing the mean to a median for consistency. I believe the running median should remain consistent across all figures (e.g., using 40 points throughout). I completely agree with employing medians in this study, as they are less susceptible to outliers. In any case, I believe that these suggested improvements will not alter the study's conclusions but will enhance the consistency of calculations and the readability of the figures.
Regarding the plots containing upstream plasma beta (histograms and running medians), the authors could consider using a logarithmic scale instead of a linear scale, as it provides a more natural representation (see, for example, Figure 1 in Chen et al. 2014, GRL, 10.1002/2014GL062009). This could improve the readability of the plots.
Lines 450-452:
I suggest including Pitna et al. 2023 (JPCS, 10.1088/1742-6596/2544/1/012009) in the discussion. They modeled upstream fluctuations as 2D turbulence (a specific set of flux ropes). Since flux rope modes, by definition, exhibit zero velocity fluctuations, an enhancement of magnetic field fluctuations within a flux rope naturally leads to a decrease in residual energyβassuming that upstream turbulence consists of a dominant 2D turbulence component and a minor slab population. The observations reported here align well with their findings.
Typos and Inaccuracies
Table 1: Fourth row: Correct the formatting of ββ¦ mean(β<> β¦β
Sentence in Lines 257-258: Please reformulate for clarity.
Figure 7: Verify the accuracy of the embedded symbols β<β and β>β in the two bottom rows.
Lines 358, 370 and other instances: Change βFRβ to βSFRβ where appropriate.
Line 401: I appreciate the approach of rectifying the cross-helicity as described in Section 2.3, where the authors assert the average Parker IMF angles of 315Β° and 135Β°. However, these angles should be quite different at distances around 0.3 AU. The authors seem to be aware of this, as the correct definition of "away" and "toward" sectors is displayed in the fourth panel of Figure 11. I suggest adjusting the angles mentioned in the text accordingly.
In conclusion, I believe this large statistical study is both novel and insightful. The statistics of identified AFs and SFRs provide a good direction for future research. A well-executed statistical study can help identify specific directions where theoretical analysis should be conducted. While the statistical sample is substantial, it is not yet large enough to fully investigate the influence of a single turbulent or shock parameter. However, this study offers valuable insights into this complex problem.
Citation: https://doi.org/10.5194/egusphere-2024-3564-RC2 -
AC2: 'Reply on RC2', Emilia Kilpua, 24 Mar 2025
We thank the reviewer for the careful reading of our manuscript and useful comments. Please find our responses from below.
Minor Comments
Lines 61-64:
I believe this sentence should be phrased more clearly. While the residual energy increases with heliocentric distance, the imbalance of the inertial range cross-helicity decreasesβi.e., it approaches zero with increasing heliocentric distance. See, for example, Figure 63 in Bruno and Carbone (2013).
This was indeed not correctly formulated to fully reflect the results of the referenced papers. Chen et al., 2020 find by analysing PSP measurements that both cross-helicity and residual energy approach zero, i.e. fluctuations becoming more balanced and equipartioned with increasing distance. In turn, Bruno and Carbone 2013 where the authors have remade the figure from Bavassano et al., 2000 based on polar solar wind measurements by Ulysses at 1.4 - 4.3 au find that the residual energy becomes increasingly negative with increasing heliospheric distance, suggesting that fluctuations becoming less equipartioned. We have now detailed this part in the paper.
Line 236:
Upon closer inspection of Figure 4, it appears that the running median differs for r_g, beta_u, etc. For example, for r_g, the black and grey curves should end between the 20th and 21st data points. However, there are only four points to the right of the curveβs endings, which suggests that the running median is calculated over eight points. For beta_u, there appear to be approximately 16 points, suggesting that the median is calculated over ~32 points. Could the authors comment on this or improve the figures?
If a mean is calculated over the x-values while the median is applied to the y-values, I suggest changing the mean to a median for consistency. I believe the running median should remain consistent across all figures (e.g., using 40 points throughout). I completely agree with employing medians in this study, as they are less susceptible to outliers. In any case, I believe that these suggested improvements will not alter the study's conclusions but will enhance the consistency of calculations and the readability of the figures.
Regarding the plots containing upstream plasma beta (histograms and running medians), the authors could consider using a logarithmic scale instead of a linear scale, as it provides a more natural representation (see, for example, Figure 1 in Chen et al. 2014, GRL, 10.1002/2014GL062009). This could improve the readability of the plots.
We thank the referee for noticing these inconsistencies regarding the figures. The x-axis values were running means and y-axis values running medians. Now both have changed to running medians in Figures 4,5, 8 and 9. The medians are calculated with 40 sliding averaged windows (except in Figure 8) so after the last median point there should be always 20 points. To enhance visibility of the median curves we had limited y-range with a few data points for some cases outside the shown range. We now mention this in the text and have also added figures 4,5, and 9 with the full x-axis ranges as Supplementary Materials. The median curves were not significantly affected by these changes. We have now plotted plasma beta on a logarithmic scale, which indeed looks much nicer that way.
Lines 450-452:
I suggest including Pitna et al. 2023 (JPCS, 10.1088/1742-6596/2544/1/012009) in the discussion. They modeled upstream fluctuations as 2D turbulence (a specific set of flux ropes). Since flux rope modes, by definition, exhibit zero velocity fluctuations, an enhancement of magnetic field fluctuations within a flux rope naturally leads to a decrease in residual energyβassuming that upstream turbulence consists of a dominant 2D turbulence component and a minor slab population. The observations reported here align well with their findings.
We now mention this paper in the discussion
Typos and Inaccuracies
Table 1: Fourth row: Correct the formatting of ββ¦ mean(β<> β¦β
Corrected
Sentence in Lines 257-258: Please reformulate for clarity.
We have now removed this sentence. It was very unclear, seemed not to convey any relevant information, and could have been left here by accident.
Figure 7: Verify the accuracy of the embedded symbols β<β and β>β in the two bottom rows.
We have now corrected the labels in Figure 7.
Lines 358, 370 and other instances: Change βFRβ to βSFRβ where appropriate.
We have made this change
Line 401: I appreciate the approach of rectifying the cross-helicity as described in Section 2.3, where the authors assert the average Parker IMF angles of 315Β° and 135Β°. However, these angles should be quite different at distances around 0.3 AU. The authors seem to be aware of this, as the correct definition of "away" and "toward" sectors is displayed in the fourth panel of Figure 11. I suggest adjusting the angles mentioned in the text accordingly.
The IMF angle has been calculated in the analysis taking into account the radial solar wind speed and radial distance from the Sun. The text only gave the average Parker winding values, and we have now explained this in Section 2.3 and give also the corresponding formula.
Citation: https://doi.org/10.5194/egusphere-2024-3564-AC2
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AC2: 'Reply on RC2', Emilia Kilpua, 24 Mar 2025
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